If you try to Google DSP, you will be confronted with a barely comprehensible
Googling DSP problems can lead to the situation where authors are barfing math on you.

There will be no equations
http://25.media.tumblr.com/tumblr_lry7eidRC41qela2qo1_500.png
Take real-world continuous measurement. Turn it into a discrete series of data points. Use an algorithm to manipulate the data samples to do cool things.

A digital signal is a signal turned into values at points in time or space

In order to be able to hold the signal in computer memory we need to be able to discretize the signal.

Sampling gets values at regular intervals

* We need to pick a time or space interval a which to collect data
* This will give us our points along the x-axis
* E.g every ms, or mm

Quantization buckets values

* We need to put our sample point into a value bucket
* E.g. if we are storing our data in an 8-bit int, we divide up the y-axis range and ask which value it's closest to
We have to do both
Having a low resolution of sampling or quantization can distort the signal
Anytime you are doing anything to that signal, that's DSP